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Discrete Mathematics, 6/E
Richard Johnsonbaugh

ISBN-10: 0131176862
ISBN-13: 9780131176867

Publisher: Pearson
Copyright: 2005
Format: Cloth; 688 pp
Published: 08/04/2004

For a one- or two-term introductory course in discrete mathematics.

This best-selling book provides an accessible introduction to discrete mathematics, using an algorithmic approach that focuses on problem-solving techniques. The new edition weaves techniques of proofs into the text as a running theme. Each chapter has a special section dedicated to showing students how to attack and solve problems.

This product accompanies:
Johnsonbaugh, Discrete Mathematics, 7/E

Enhanced pedagogy throughout—Includes examples, exercises, figures, tables, sections on problem-solving, section reviews, notes, chapter reviews, self-tests, and computer exercises to help students master introductory discrete mathematics.

Strong emphasis on reading and doing proofs—Illustrates most proofs of theorems with annotated figures to provide additional explanation and insight into the proofs.

Thorough discussion of algorithms, recursive algorithms, and the analysis of algorithms (Ch. 3)—The algorithms are written in a flexible form of pseudocode.

Over 500 worked examples throughout the text—Helps students understand the material.

Over 3500 exercises—Approximately one third have answers.

A large number of applications with an emphasis on computer science—Helps motivate the material.

A strong emphasis on the interplay among the various topics—E.g., mathematical induction is closely tied to recursive algorithms; the Fibonacci sequence is used in the analysis of the Euclidean algorithm; many exercises throughout the book require mathematical induction; demonstrations of how to characterize the components of a graph by defining an equivalence relation on the set of vertices; and more.

Figures and tables—Illustrate concepts, show how algorithms work, elucidate proofs, and motivate the material. Several figures illustrate proofs of theorems. Figure captions provide additional explanation and insight into the proofs.

Summaries of the mathematical and algorithm notation used in the book—Found in the inside covers.

NEW - Reorganization of Chapters 1 and 2—Chapter 1 now contains basic terminology: sets, functions, sequences, strings, and relations. Logic, extensively expanded and revised, is moved to Chapter 2. This reorganization allows the concepts of Chapter 1 to be used in the discussion of logic, thus better motivating and illustrating logic.

NEW - New chapter on introductory number theory (Ch. 4) —Integrates material on the Euclidean algorithm and expanded material on RSA public-key cryptosystem into this new chapter.

NEW - New chapter on probability (Ch. 6) —Includes new material on probability.

NEW - More Problem-Solving Corners—Helps students solve problems and do proofs.

NEW - A consistent Web icon used throughout—Indicates that more explanation and examples about a particular topic can be found on the Johnsonbaugh Companion Website (http://condor.depaul.edu/~rjohnson), or another relevant Web site.

NEW - More worked examples and exercises.

NEW - Enhanced Companion Website (http://condor.depaul.edu/~rjohnson)—Contains expanded explanations of difficult material, links to other sites for additional information about discrete mathematics topics, PowerPoint slides, a sample chapter, supplementary material, computer programs, and an errata list.

Expanded Chapter 1–Chapter 1 now contains more background material and more depth on logic and proof.

New Chapter 3–The topic of Relations has been expanded and set into a seperate chapter.

New chapter on introductory number theory (Ch. 4)–Integrates material on the Euclidean algorithm and expanded material on RSA public-key cryptosystem into this new chapter.

More Problem-Solving Corners–Helps students solve problems and do proofs (pg. 63-65, 171-173).

A consistent Web icon used throughout–Indicates that more explanation and examples about a particular topic can be found on the Johnsonbaugh Companion Website (http://condor.depaul.edu/~rjohnson), or another relevant Web site.

More worked examples (increased from 500 to 600) and exercises (increased from 3500 to 4000).

Enhanced Companion Website (http://condor.depaul.edu/~rjohnson)–Contains expanded explanations of difficult material, links to other sites for additional information about discrete mathematics topics, PowerPoint slides, a sample chapter, supplementary material, computer programs, and an errata list.

(NOTE: All Chapters end with Notes, Chapter Review, Chapter Self-Test, and Computer Exercises.)

Preface.

1. Logic and Proofs.

Propositions. Conditional Propositions and Logical Equivalence. Quantifiers. Proofs. Resolution Proofs. Mathematical Induction. Strong Form of Induction and well ordering Property.

2. The Language of Mathematics

Sets. Functions. Sequences and Strings. Relations.

3. Relations.

Relations. Equivalence Relations. Matrices of Relations. Relational Databases.

4. Algorithms.

Introduction. Correctness of Algorithms. Analysis of Algorithms. Recursive Algorithms.

5. Introduction to Number Theory.

Divisors. Representation of Integers and Integer Algorithims. The Euclidean Algorithm. The RSA Public-Key Cryptosystem.

6. Counting Methods and the Pigeonhole Principle.

Basic Principles. Permutations and Combinations. Algorithms for Generating Permutations and Combinations. Introduction to Discrete Probability. Discrete Probability Theory. Generalized Permutations and Combinations. Binomial Coefficients and Combinatorial Identities. The Pigeonhole Principle.

7. Recurrence Relations.

Introduction. Solving Recurrence Relations. Applications to the Analysis of Algorithms.

8. Graph Theory.

Introduction. Paths and Cycles. Hamiltonian Cycles and the Traveling Salesperson Problem. A Shortest-Path Algorithm. Representations of Graphs. Isomorphisms of Graphs. Planar Graphs. Instant Insanity.

9. Trees.

Introduction. Terminology and Characterizations of Trees. Spanning Trees. Minimal Spanning Trees. Binary Trees. Tree Traversals. Decision Trees and the Minimum Time for Sorting. Isomorphisms of Trees. Game Trees.

10. Network Models.

Introduction. A Maximal Flow Algorithm. The Max Flow, Min Cut Theorem. Matching.

11. Boolean Algebras and Combinatorial Circuits.

Combinatorial Circuits. Properties of Combinatorial Circuits. Boolean Algebras. Boolean Functions and Synthesis of Circuits. Applications

12. Automata, Grammars, and Languages.

Sequential Circuits and Finite-State Machines. Finite-State Automata. Languages and Grammars. Nondeterministic Finite-State Automata. Relationships Between Languages and Automata.

13. Computational Geometry.

The Closest-Pair Problem. An Algorithm to Compute the Convex Hull.

Appendices.

Matrices. Algebra Review.

References.

Hints and Solutions to Selected Exercises.

Index.

Discrete Math (Mathematics)

Discrete Mathematics, 7/E
Johnsonbaugh
©2009 | Pearson | Cloth; 792 pp | Instock
ISBN-10: 0131593188 | ISBN-13: 9780131593183
Net price: $96.00 (What's this?)Brief Description

For a one- or two-term introductory course in discrete mathematics.

Focused on helping students understand and construct proofs and expanding their mathematical maturity, this best-selling text is an accessible introduction to discrete mathematics. Johnsonbaugh’s algorithmic approach emphasizes problem-solving techniques. The Seventh Edition reflects user and reviewer feedback on both content and organization.

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Discrete Source
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©2009 | Pearson | On-line Supplement | Instock
ISBN-10: 0321625242 | ISBN-13: 9780321625243

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